US20090077156A1 - Efficient constraint monitoring using adaptive thresholds - Google Patents

Efficient constraint monitoring using adaptive thresholds Download PDF

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US20090077156A1
US20090077156A1 US12/010,942 US1094208A US2009077156A1 US 20090077156 A1 US20090077156 A1 US 20090077156A1 US 1094208 A US1094208 A US 1094208A US 2009077156 A1 US2009077156 A1 US 2009077156A1
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local
constraint
remote site
network
global
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Srinivas Raghav Kashyap
Rajeev Rastogi
S. R. Jeyashankher
Pushpraj Shukla
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Nokia of America Corp
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Lucent Technologies Inc
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    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B18/00—Surgical instruments, devices or methods for transferring non-mechanical forms of energy to or from the body
    • A61B18/04—Surgical instruments, devices or methods for transferring non-mechanical forms of energy to or from the body by heating
    • A61B18/12—Surgical instruments, devices or methods for transferring non-mechanical forms of energy to or from the body by heating by passing a current through the tissue to be heated, e.g. high-frequency current
    • A61B18/14—Probes or electrodes therefor
    • A61B18/1442—Probes having pivoting end effectors, e.g. forceps
    • A61B18/1445—Probes having pivoting end effectors, e.g. forceps at the distal end of a shaft, e.g. forceps or scissors at the end of a rigid rod
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B18/00—Surgical instruments, devices or methods for transferring non-mechanical forms of energy to or from the body
    • A61B18/04—Surgical instruments, devices or methods for transferring non-mechanical forms of energy to or from the body by heating
    • A61B18/12—Surgical instruments, devices or methods for transferring non-mechanical forms of energy to or from the body by heating by passing a current through the tissue to be heated, e.g. high-frequency current
    • A61B18/14—Probes or electrodes therefor
    • A61B18/1402—Probes for open surgery
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B17/00—Surgical instruments, devices or methods, e.g. tourniquets
    • A61B2017/0046—Surgical instruments, devices or methods, e.g. tourniquets with a releasable handle; with handle and operating part separable
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B17/00—Surgical instruments, devices or methods, e.g. tourniquets
    • A61B17/28—Surgical forceps
    • A61B17/29—Forceps for use in minimally invasive surgery
    • A61B2017/2926—Details of heads or jaws
    • A61B2017/2945—Curved jaws
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B18/00—Surgical instruments, devices or methods for transferring non-mechanical forms of energy to or from the body
    • A61B2018/00571—Surgical instruments, devices or methods for transferring non-mechanical forms of energy to or from the body for achieving a particular surgical effect
    • A61B2018/00607—Coagulation and cutting with the same instrument
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B18/00—Surgical instruments, devices or methods for transferring non-mechanical forms of energy to or from the body
    • A61B18/04—Surgical instruments, devices or methods for transferring non-mechanical forms of energy to or from the body by heating
    • A61B18/12—Surgical instruments, devices or methods for transferring non-mechanical forms of energy to or from the body by heating by passing a current through the tissue to be heated, e.g. high-frequency current
    • A61B18/14—Probes or electrodes therefor
    • A61B2018/1405—Electrodes having a specific shape
    • A61B2018/1425—Needle
    • A61B2018/1432—Needle curved

Definitions

  • network monitoring systems When monitoring emerging large-scale, distributed systems (e.g., peer to peer systems, server clusters, Internet Protocol (IP) networks, sensor networks and the like), network monitoring systems must process large volumes of data in (or near) real-time from a widely distributed set of sources. For example, in a system that monitors a large network for distributed denial of service (DDoS) attacks, data from multiple routers must be processed at a rate of several gigabits per second. In addition, the system must detect attacks immediately after they happen (e.g., with minimal latency) to enable networks operators to take expedient countermeasures to mitigate effects of these attacks.
  • DDoS distributed denial of service
  • FIG. 1 illustrates a conventional distributed monitoring method utilizing what is referred to as a zero-slack scheme.
  • a central coordinator such as a network operations center s 0 assigns local constraint threshold values T i to each remote site s 1 , . . . , s n according to Equation (1) shown below.
  • T is a global constraint threshold value for the system and n is the number of nodes or remote sites in the system.
  • the global constraint threshold corresponds to the total number of bytes that passed the service provider network in the past second.
  • FIG. 1 illustrates a conventional distributed monitoring method. The method shown in FIG. 1 will be discussed with regard to the conventional system architecture shown in FIG. 2 .
  • variable x j may be the total amount of traffic (e.g., in bytes) entering into a network through an ingress point.
  • the variable x j may also be an observed number of cars on the highway, an amount of traffic from a monitored network in a day, the volume of remote login (e.g., TELNET, FTP, etc.) requests received by hosts within the organization that originate from the external hosts, packet loss at a given remote site or network node, etc.
  • step S 506 when the coordinator s 0 receives the local alarm transmission from site s j , the coordinator s 0 calculates an estimate of the global aggregate value according to Equation (2) shown below.
  • each local constraint T i represents an estimate of the current value of variable x i at each node other than x j , which are known at the central coordinator s 0 .
  • the central coordinator s 0 determines whether Equation (3) is satisfied.
  • the central coordinator s 0 sends a message requesting current values of the variable x i to each remote site s 1 , . . . , s n at step S 510 .
  • This transmission of messages is referred to as a “global poll.”
  • each remote site sends an update message including the current value of the variable x i .
  • the central coordinator s 0 determines if the global network constraint threshold T has been violated at step S 512 .
  • the central coordinator s 0 aggregates the values for variables x 1 , x 2 , . . . x n and compares the aggregate value with the global constraint threshold. If the aggregate value is greater than the global constraint threshold, then the central coordinator s 0 determines that the global constraint threshold T is violated. If the central coordinator s 0 determines that the global constraint threshold T is violated, the central controller s 0 records violation of the global constraint threshold in a memory at step S 514 . In one example, the central controller s 0 may generate a log, which includes time, date, and particular values associated with the constraint threshold violation.
  • step S 512 if the central coordinator s 0 determines that the global constraint threshold Tis not violated, the process terminates and no action is taken.
  • step S 508 if the central coordinator s 0 determines that Equation (3) is satisfied, the central coordinator s 0 determines that a global poll is not necessary, the process terminates and no action is taken.
  • This method is an example of a zero slack scheme in which the sum of the local thresholds T i for all remote sites in the network is equal to the global constraint threshold T, or in other words,
  • a local alarm transmission results in a global poll by the central coordinator s 0 because any violation of a local constraint threshold for any node causes the central coordinator s 0 to estimate that the global constraint threshold T is violated.
  • Using a zero-slack scheme results in relatively high communication costs due to the frequency of local alarms and global polls.
  • Example embodiments provide methods for tracking anomalous behavior in a network referred to as non-zero slack schemes, which may reduce the number of communication messages in the network (e.g., by about 60%) necessary to monitor emerging large-scale, distributed systems using distributed computation algorithms.
  • system behavior e.g., global polls
  • system behavior is determined by multiple values at the various sites, and not a single value as in the conventional art.
  • At least one illustrative embodiment uses Markov's Inequality to obtain a simple upper bound that expresses the global poll probability as the sum of independent components, one per remote site involving the local variable plus constraint at the remote site.
  • optimal local constraints e.g., the local constraints that minimize communication costs
  • Non-zero slack schemes may result in lower communication costs.
  • FIG. 1 illustrates a conventional method for distributed monitoring
  • FIG. 2 is a conventional system architecture
  • FIG. 3 is a flow chart illustrating a method for generating and assigning local constraints to remote sites in a system according to an illustrative embodiment
  • FIG. 4 is a flow chart illustrating a method for generating a local constraint using the Markov-based algorithm according to an illustrative embodiment
  • FIG. 5 is a flow chart illustrating a method for generating a local constraint for a remote site using a reactive algorithm according to an illustrative embodiment.
  • Illustrative embodiments are directed to methods for generating and/or assigning local constraints to nodes or remote sites within a network and methods for tracking anomalous behavior using the assigned local constraint thresholds.
  • Anomalous behavior may be used to indicate that action is required by a network operator and/or system operations center.
  • the methods described herein utilize non-zero slack scheme algorithms for determining local constraints that retain some slack in the system.
  • DSPs digital signal processors
  • ASICs application-specific-integrated-circuits
  • FPGAs field programmable gate arrays
  • each remote site is assigned a local constraint (or threshold) T i such that
  • the slack SL refers to the difference between the global threshold value and the sum of the remote site threshold values in the system. More particularly, the slack is given by
  • the global constraint may be decomposed into a set of local thresholds, T i at each remote site s i .
  • local constraint values hereinafter local constraints
  • T i may be generated and/or assigned such that
  • ⁇ i 1 n ⁇ T i ⁇ T .
  • an “uninteresting” event is a change in value at some remote site that does not cause a global function to exceed a threshold of interest.
  • One embodiment provides a method for assigning local constraints to nodes in a system using a “brute force” algorithm.
  • the method may be performed at the central coordinator s 0 in FIG. 1 .
  • FIG. 3 is a flow chart illustrating a method for generating and assigning local constraints to remote sites in a system according to an illustrative embodiment.
  • the communication between the central coordinator s 0 and each remote site s i may be performed concurrently.
  • the central coordinator s 0 receives histogram updates in an update message.
  • variable x i may be the total amount of traffic (e.g., in bytes) entering into a network through an ingress point.
  • variable x i may also be an observed number of cars on the highway, an amount of traffic from a monitored network in a day, the volume of remote login (e.g., TELNET, FTP, etc.) requests received by hosts within the organization that originate from the external hosts, packet loss at a given remote site or network node, etc.
  • the volume of remote login e.g., TELNET, FTP, etc.
  • each remote site si maintains a histogram of the constantly changing value of its local variable x i observed over time as H i (v), ⁇ v ⁇ [0, T], where H i (v) is the probability of variable x i having a value v).
  • the update messages may be sent and received periodically, wherein the period is referred to as the recompute interval.
  • the central coordinator s 0 in response to receiving the update messages from the remote sites, the central coordinator s 0 generates (calculates) local constraints T i for each remote site s i .
  • the central coordinator s 0 may generate local constraints T i based on a total system cost C as will be described in more detail below.
  • the coordinator s 0 first calculates a probability P l (i) of a local alarm for each individual remote site (hereinafter local alarm probability) according to Equation (4) shown below.
  • Equation (4) Pr(x i >T i ) is the probability that the observed value at remote site s i is greater than its threshold T i and is independently calculated for a given local constraint T i .
  • the local alarm probability P l (i) is entirely independent of the state of the other remote sites.
  • the local alarm probability P l (i) for each remote site s i is independent of values of variable x i at other remote sites in the system.
  • the central coordinator s 0 determines a probability P g of a global poll (hereinafter referred to as a global poll probability) in the system according to Equation (5) shown below:
  • Y i is an estimated value for x i at each remote site s i in the system.
  • the estimated values Y i are stored at the coordinator s 0 such that Y i ⁇ x i at all times.
  • the central coordinator s 0 updates the stored values Y i based on values x i reported in local alarms from each remote site.
  • the coordinator s 0 receives updates for values x i at remote site s i via a local alarm message generated by remote site s i once the observed value x i exceeds its local constraint T i .
  • the stored values Y i at the central coordinator s 0 for each remote site may be summarized as:
  • Y i ⁇ x i ⁇ ⁇ for ⁇ ⁇ each ⁇ ⁇ s i ⁇ ⁇ that ⁇ ⁇ reports ⁇ ⁇ a ⁇ ⁇ local ⁇ ⁇ alarm ; and T i ⁇ ⁇ for ⁇ ⁇ each ⁇ ⁇ s i ⁇ ⁇ that ⁇ ⁇ has ⁇ ⁇ not ⁇ ⁇ reported ⁇ ⁇ anything .
  • O(nT 2 ) is a standard notation indicating running time of an algorithm.
  • the global alarm probability P g is dependent on the state of all remote sites in the system. In other words, the global alarm probability P g is dependent on values of variable x i at other remote sites in the system.
  • the central coordinator s 0 generates the local threshold T i for remote site s i based on the total system cost C given by Equation (6) shown below.
  • Equation (6) P l (i) is the local alarm probability at site s i , P g is the global poll probability, C l is the cost of a local alarm transmission message from remote site s i to the coordinator s 0 and C g is the cost of performing a global poll by the central coordinator s 0 .
  • C l is O(l) and C g is O(n), where O(l) and O(n) differ by orders of magnitude.
  • O(l) is a constant independent of the size of system and O(n) is a quantity that grows linearly with the size of the system.
  • C l may be a first value (e.g., 10) and C g is another value (e.g., 100).
  • C l may be a first value (e.g., 10) and C g is another value (e.g., 100).
  • C l remains close to 10, but C g increases much larger than 100.
  • C g grows much faster than C l as network size increases.
  • the central coordinator s 0 generates local constraints T i for each remote site s i to minimize the total system cost C.
  • the central coordinator s 0 performs a naive exhaustive enumeration of all T n possible sets of local threshold values to generate the local constraints at each remote site that result in minimum total system cost C.
  • the local alarm probability P l (i) at each remote site s i and the global poll probability P g value are calculated to determine the total system cost C.
  • this naive enumeration has a running time of O(nT n+2 ).
  • the small constant ⁇ may be determined experimentally and assigned, for example, by a network operator at a network operations center.
  • step S 206 the central coordinator s 0 sends each generated local constraint T i to its corresponding remote site s i .
  • Another illustrative embodiment provides a method for generating local constraints using a Markov-based algorithm.
  • This embodiment uses Markov's inequality to approximate the global poll probability P g resulting in a decentralized algorithm, in which each site s i may independently determine its own local constraint T i .
  • Markov's inequality gives an upper bound for the probability that a non-negative function of a random variable is greater than or equal to some positive constant.
  • FIG. 4 is a flow chart illustrating a method for generating a local constraint using the Markov-based algorithm according to an illustrative embodiment. As noted above, the method shown in FIG. 4 may be performed at each individual remote site in the system.
  • remote site s i approximates a global poll probability P g according to Equation (7) shown below.
  • the approximation of the global poll probability P g obtained by the remote site s i represents the upper bound on the global poll probability P g .
  • the remote site s i estimates the total system cost C using Equation (8) shown below.
  • Equation (9) the remote site's estimated individual contribution to the total system cost E[Y i ] is given by Equation (9) shown below.
  • the remote site s i independently determines the local constraint T i based on its estimated individual contribution E[Y i ] to the estimated total system cost C given by Equation (8). More specifically, for example, the remote site s i independently calculates the local constraint T i that minimizes its contribution to the estimated total system cost C, thus allowing the remote site s i to calculate its local constraint T i independent of the coordinator s 0 .
  • the remote site s i may calculate its local constraint T i by performing a linear search in the range 0 to T. Because such a search requires O(T) running time, the running time may be reduced to O( ⁇ ) by searching for the optimal threshold value in a small range [T i ⁇ , T i + ⁇ ].
  • the linear search performed by the remote site s i may be performed at least once during each round or recompute interval. Each time remote site s i recalculates its local constraint T i , the remote site s i reports the newly calculated local constraint to the central coordinator s 0 via an update message.
  • each remote site in the system is allowed to independently determine their local threshold values, ensuring that
  • each remote site's local constraint may be restricted to a maximum of T/n by the central coordinator s 0 .
  • a restriction may reduce performance in cases where one site's value is very high on average compared to other sites.
  • the coordinator s 0 may determine if
  • the coordinator s 0 may reduce each threshold value T j by
  • Another illustrative embodiment provides a method for generating local constraints using what is referred to herein as a “reactive algorithm.”
  • the method for generating local constraints using the reactive algorithm may be performed at each remote site individually or at a central location such as central coordinator s 0 .
  • each remote site reports the newly calculated local constraint to the central coordinator in an update message during each recompute interval. If the method according to this illustrative embodiment is performed at the central coordinator s 0 , then the central coordinator s 0 assigns and sends the newly calculated local constraint to each remote site during each recompute interval. As noted above, the central coordinator s 0 and the remote sites may communicate in any well-known manner.
  • this embodiment will be described with regard to FIG. 1 , in particular, with the method being executed at remote site s i .
  • the remote site s i determines its own local constraint T i based on actual local alarm and global poll events within the system.
  • FIG. 5 is a flow chart illustrating a method for generating a local constraint for a remote site using a reactive algorithm according to an illustrative embodiment.
  • the remote site s i generates an initial local constraint T i , for example, using the above described Markov-based algorithm.
  • the remote site s i then adjusts the local constraint T i based on actual global poll and local alarm events in the system.
  • the remote site s i determines that the local constraint T i may be lower than an optimal value.
  • the remote site s i may increase its local constraint T i value by a factor ⁇ with a probability 1/ ⁇ i (or 1, if 1/ ⁇ i is greater than 1), where ⁇ and ⁇ i are parameters of the system greater than 0.
  • system parameter ⁇ is a constant selected by a network operator at the network operations center and is indicative of the rate of convergence.
  • Parameter ⁇ i is computed according to Equation (10) discussed in more detail below.
  • the remote site s i determines that its local constraint T i may be higher than an optimal value.
  • the remote site s i may reduce the threshold value by a factor of ⁇ with a probability ⁇ i (or 1, if ⁇ i is greater than 1).
  • the local constraint at remote site s i is not always decreased in response to a global poll, but rather is decreased probabilistically.
  • parameter ⁇ i may be set according to Equation (10) shown below.
  • probability P l (T i opt ) is the local alarm probability when the local threshold is set to T i opt and the probability P g opt is the global probability when all remote sites take the optimal local constraint values.
  • Equation (10) can be shown to be a valid value for ⁇ i because if each remote site s i does not have an optimal local constraint T i opt , then either (A) the current local constraint T i ′>T i opt , P l (T i ′) ⁇ P l (T i opt ) and P g (T i ′)>P g (T i opt ), or (B) current local constraint T i ′ ⁇ T i opt , P l (T i ′)>P l (T i opt ) and P g (T i ′) ⁇ P g (T i opt ).
  • the average number of observed local alarms is less than ⁇ i times the average number of observed global polls.
  • the local constraint value decreases over time from T i l .
  • the threshold value will increase if the threshold is less than T i opt .
  • the stable state of the system is reached when local constraints are optimized (e.g., T i opt ) using the reactive algorithm. Once the system reaches a stable state (at the optimal setting of local constraints), the communication overhead is minimized compared to all other states.
  • the remote site s i may utilize the Markov-based method to determine the local constraint T i that minimizes the total system cost C and use this value to compute the contribution of the remote site to P g .
  • the remote site s i sends its individual estimated contribution E[Y i ] of P g to the central coordinator s 0 at least once during or at the end of each recompute interval.
  • the central coordinator s 0 sums (or aggregates) the components of P g received from the remote sites and computes the P g value.
  • the coordinator s 0 sends this value of P g to each remote site, and each remote site uses this received value of P g to compute parameter ⁇ i .
  • Illustrative embodiments use an estimate of P g provided by the central coordinator s 0 to compute ⁇ i at each remote site. The remaining portions of information necessary are available locally at each remote site.
  • the above discussed embodiments may be used to generate and/or assign local thresholds to remote sites in the system of FIG. 2 , for example. Using these assigned local thresholds, methods for distributed monitoring may be performed more efficiently and system costs may be reduced. In one example, the local thresholds determined according to illustrative embodiments may be utilized in the distributed monitoring method discussed above with regard to FIG. 1 .
  • illustrative embodiments may be used to monitor the total amount of traffic flowing into a service provider network.
  • the monitoring setup includes acquiring information about ingress traffic of the network. This information may be derived by deploying passive monitors at each link or by collecting flow information (e.g., Netflow records) from the ingress routers (remote sites). Each monitor determines the total amount of traffic (e.g., in bytes) coming into the network through that ingress point. If the total amount of traffic exceeds a local constraint assigned to that ingress point, the monitor generates a local alarm. A network operations center may then perform a global poll of the system, and determine whether the total traffic across the system violates a global threshold, that is, a maximum total traffic through the network.
  • flow information e.g., Netflow records
  • ⁇ i 1 n ⁇ ( - log ⁇ ( 1 - l i ) ) ⁇ - log ⁇ ( 0.99 ) .
  • ⁇ log(1 ⁇ l i ) is local constraint T i and ⁇ log(0.99) is global constraint T.
  • the losses may be monitored in a network using distributed constraints monitoring. Delays can be monitored similarly using distributed SUM constraints.
  • illustrative embodiments may be used to raise an alert when the total number of cars on the highway exceeds a given number and report the number of vehicles detected, identify all destinations that receive more than a given amount of traffic from a monitored network in a day, and report their transfer totals, monitor the volume of remote login (e.g., TELNET, FTP, etc.) request received by hosts thin the organization that originate from the external hosts, etc.
  • remote login e.g., TELNET, FTP, etc.
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